It found that rents were 4.9% up on March 2010 and at their highest level since November last year.
LSL said that if rents continue at their current rate of increase, they will hit £715 by this time next year.
The highest monthly increases in rent were in East England at 2.2% and the South East at 1.7%.
Yet, on an annual basis, London has outstripped all other areas, seeing rents increase 7.3%, with the South East close behind at 6.7%.
However, the South West recorded a fall in average rents of 1.6%, followed by the West Midlands, down by 1.3%. Wales and Yorkshire and the Humber also recorded small monthly drops.
Nevertheless, over the past year, only the South West and Wales have registered annual falls in rent, down 2.4% and 1.5% respectively.
LSL said that rising rents have counteracted an annual decrease of 1.8% in rental property prices, with annual returns remaining steady at 2.6%. LSL estimated that the total annual return is now equivalent to £4,261 to £7,326 in rent, with a capital loss of £3,065.
Meanwhile, tenant arrears in March significantly improved, falling to 9.4% of all UK rent in arrears compared to 12.6% in February.
Unpaid rent totalled £224m across the UK in March, the lowest figure since October 2010.
David Brown, commercial director of LSL Property Services, said: “Landlords are seeing demand for their properties go from strength to strength. Although more high LTV products are coming onto the market, there is still not much money at that level from lenders, and first-time buyers simply can’t afford the average £25,000 deposit lenders require without substantial aid from parents.”
He added: “Most would-be first-timers are remaining in rented accommodation for nearly a decade. The growing demand continues to outstrip supply, and this is pushing rents upwards beyond the rate of inflation and well above wage rises.
“At the current rate of increase, the average rent will top £715 this time next year.”
